Affiliation:
1. Nanyang Technological University, Singapore
2. Google Inc., Mountain View, CA
3. City of Hope, National Medical Center, USA
4. University of California at Riverside
Abstract
We introduce a new combinatorial optimization problem in this article, called the
minimum common integer partition
(MCIP) problem, which was inspired by computational biology applications including ortholog assignment and DNA fingerprint assembly. A
partition
of a positive integer
n
is a multiset of positive integers that add up to exactly
n
, and an
integer partition
of a multiset
S
of integers is defined as the multiset union of partitions of integers in
S
. Given a sequence of multisets
S
1
,
S
2
, …,
S
k
of integers, where
k
≥ 2, we say that a multiset is a
common integer partition
if it is an integer partition of every multiset
S
i
, 1 ≤
i
≤
k
. The MCIP problem is thus defined as to find a common integer partition of
S
1
,
S
2
, …,
S
k
with the minimum cardinality, denoted as MCIP(
S
1
,
S
2
, …,
S
k
). It is easy to see that the MCIP problem is NP-hard, since it generalizes the well-known subset sum problem. We can in fact show that it is APX-hard. We will also present a 5/4-approximation algorithm for the MCIP problem when
k
= 2, and a 3
k
(
k
−1)/3
k
−2-approximation algorithm for
k
≥ 3.
Funder
National Institutes of Health
National Science Foundation
Division of Information and Intelligent Systems
National Natural Science Foundation of China
Publisher
Association for Computing Machinery (ACM)
Subject
Mathematics (miscellaneous)
Cited by
11 articles.
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